Vargas went 0-for-4 in Tuesday's 4-3 loss to the Royals.
Vargas made his debut with the White Sox after being traded from the Dodgers on Monday. He served as the designated hitter and hit second in the lineup. The White Sox could eventually have Vargas see time at third base, second base or in the corner outfield, and the final two months of the campaign should offer him the opportunity for his most consistent playing time in the majors.